Trimmed-Robust State Space Model Fit

Fits a robust state space model by minimizing a trimmed loss function as per Crevits and Croux (2018). A fixed proportion of the largest residuals are excluded from the objective, providing robustness against extreme outliers. The predicted observations used in the trimmed loss are computed using the Huber robust filter from Cipra and Romera (1997).

Usage

trimmed_robust_SSM(
  y,
  init_par,
  build,
  alpha,
  lower = NA,
  upper = NA,
  control = list(parscale = init_par)
)

Arguments

y

A numeric matrix of observations (time points in rows).

init_par

A numeric vector of initial parameter values.

build

A function that returns a dlm model given a parameter vector. The specify_SSM() function can be used to create this build function.

alpha

Numeric value in the interval [0, 1) indicating the trimming proportion (i.e., the proportion of data to exclude as outliers).

lower

Optional numeric vector of lower bounds for parameter estimation. Defaults to -Inf. Must be of same length as init_par.

upper

Optional numeric vector of upper bounds for parameter estimation. Defaults to Inf. Must be of same length as init_par.

control

Optional list of control parameters passed to optim. Default is list(parscale = init_par), which can help the optimizer if parameters are on vastly different scales.

Value

An object of class trimmed_robust_SSM containing the optimization result, trimming level \(\alpha\), the original data, and the original build function.

References

Crevits R. and Croux C. (2018). Robust Estimation of Linear State Space Models. *Communications in Statistics: Simulation and Computation*

Cipra, T., Romera, R. (1997). Kalman filter with outliers and missing observations. *Test* 6, 379–395. https://doi.org/10.1007/BF02564705

See also

huber_robust_SSM, roams_SSM, optim, attach_insample_info, oos_filter, specify_SSM